Rocha, J. LeonelAleixo, Sandra2013-10-262013-10-262013-04ROCHA, J. Leonel; AlLEIXO, Sandra M. - An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models. Mathematical Biosciences and Engineering. ISSN 1547-1063. Vol. 10, nr 2 (2013), p. 379-398.1547-106310.3934/mbe.2013.10.379http://hdl.handle.net/10400.21/2795In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.engGrowth modelsExtreme value lawsBeta* (p, q) densitiesBifurcations and chaosSymbolic dynamicsTopological entropyTumour dynamicsLogistic ModelTumor-GrowthImmunotherapyjournal article